1.

If Ts=1+9+9^2+9^3+9^4......+9^100 and unit digit of Ts is n then find n+9

Answer»

Other METHOD :
Final Answer : 1

T(s) = 1+ 9 + 9^2 + ........9^100.

Steps:
1) Factorise the EXPRESSION.
2) Units digit of 10 is 0 .

Now,
= > 1 +9 + {9}^{2} + {9}^{3} +..... {9}^{100} \\ = > 1 + 9(1 + 9) + {9}^{3} (1 + 9) + \\ ..... {9}^{99} (1 + 9) \\ = > 1 + (1 + 9)(9 + {9}^{3} + ..... {9}^{99} ) \\ = > 1 + 10(9 + {9}^{3} + {9}^{5} + .... {9}^{99} ) \\ = > 1 + <klux>MULTIPLE</klux> \: of \: 10. \\

Now,
Units digit of T(s):
= units digit of (1+ multiple of 10)
= units digit of (1+0)
= 1 .

Therefore, n= 1.

And (n+9) = 1+9=10.


Discussion

No Comment Found

Related InterviewSolutions